Diffusion, convection, adsorption, and reaction of chemicals in porous media (Q808949)

The authors apply homogenization techniques to the complex phenomenon of an incompressible flow through a porous medium accompanied by diffusion- convection and diffusion-reaction. Starting from the usual assumption that the system consists of a periodic array of cells with a scale factor \(\epsilon\), first the equations for the micromodel are written, describing the various phenomena in a single cell (i.e. a grain \(+\) the liquid phase), namely: a) the flow, for which Stokes equation is assumed, imposing no-slip conditions on the boundary of the grains, b) the convection-diffusion of a solute, c) the reaction- diffusion on the surface of the skeleton. Of course there is a coupling between the boundary conditions for b) and the reaction term for c) (which is assumed to be linear). The authors develop a complete theory, deriving several estimates on the solutions of the micromodel equations which allow them to show their convergence as \(\epsilon\to 0\) (in a suitable sense) to the solution of the macromodel equation. A comrehensive list of references is given.